Countries often have private information about their willingness to pay for protecting the climate system and their cost of emission reductions. We use a principal-agent model to re-examine the economic case for unilateral action by individual countries, in our case of the principal. We find that the incentive structure that arises in an incomplete information framework can motivate (i) unilateral action before contract negotiations, (ii) optimal contracts in which the principal accepts higher marginal abatement costs for herself, as well as (iii) overcompliance by the principal after the contract has been negotiated. Multilateral externalities and type-dependent outside options, which are characteristic for climate policies, play a crucial role to explain these results.